%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV491^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:38:44 AM UTC 2026
% Result : Theorem 0.22s 0.34s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV491^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n018.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 15:55:11 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.34 % (257390)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.34 % (257406)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3197377567:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.34 % (257407)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.34 % (257407)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.34 % (257401)lrs+10_16_si=on:nwc=1.5:random_seed=3596644382:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.34 % (257402)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=792135410:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.34 % (257400)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4052952631:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.34 % (257405)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=95022292:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.34 % (257403)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4254586531:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.34 % (257407)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1250534444:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.34 % (257402)Instruction limit reached!
% 0.22/0.34 % (257402)------------------------------
% 0.22/0.34 % (257402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (257402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (257402)CaDiCaL version: 2.1.3
% 0.22/0.34 % (257402)Termination reason: Instruction limit
% 0.22/0.34 % (257402)Termination phase: Saturation
% 0.22/0.34 % (257402)Time elapsed: 0.002 s
% 0.22/0.34 % (257402)Peak memory usage: 11 MB
% 0.22/0.34 % (257402)Instructions burned: 3 (million)
% 0.22/0.34 % (257401)Instruction limit reached!
% 0.22/0.34 % (257401)------------------------------
% 0.22/0.34 % (257401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (257401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (257401)CaDiCaL version: 2.1.3
% 0.22/0.34 % (257401)Termination reason: Instruction limit
% 0.22/0.34 % (257401)Termination phase: Saturation
% 0.22/0.34 % (257401)Time elapsed: 0.011 s
% 0.22/0.34 % (257401)Peak memory usage: 12 MB
% 0.22/0.34 % (257401)Instructions burned: 18 (million)
% 0.22/0.34 % (257406)Instruction limit reached!
% 0.22/0.34 % (257406)------------------------------
% 0.22/0.34 % (257406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (257406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (257406)CaDiCaL version: 2.1.3
% 0.22/0.34 % (257406)Termination reason: Instruction limit
% 0.22/0.34 % (257406)Termination phase: Saturation
% 0.22/0.34 % (257406)Time elapsed: 0.022 s
% 0.22/0.34 % (257406)Peak memory usage: 12 MB
% 0.22/0.34 % (257406)Instructions burned: 75 (million)
% 0.22/0.34 % (257405)Instruction limit reached!
% 0.22/0.34 % (257405)------------------------------
% 0.22/0.34 % (257405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (257405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (257405)CaDiCaL version: 2.1.3
% 0.22/0.34 % (257405)Termination reason: Instruction limit
% 0.22/0.34 % (257405)Termination phase: Saturation
% 0.22/0.34 % (257405)Time elapsed: 0.014 s
% 0.22/0.34 % (257405)Peak memory usage: 12 MB
% 0.22/0.34 % (257405)Instructions burned: 26 (million)
% 0.22/0.34 % (257425)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=280156164:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.34 % (257425)Instruction limit reached!
% 0.22/0.34 % (257425)------------------------------
% 0.22/0.34 % (257425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (257425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (257425)CaDiCaL version: 2.1.3
% 0.22/0.34 % (257425)Termination reason: Instruction limit
% 0.22/0.34 % (257425)Termination phase: Saturation
% 0.22/0.34 % (257425)Time elapsed: 0.002 s
% 0.22/0.34 % (257425)Peak memory usage: 11 MB
% 0.22/0.34 % (257425)Instructions burned: 3 (million)
% 0.22/0.34 % (257433)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4122274019:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.34 % (257432)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.34 % (257433)Instruction limit reached!
% 0.22/0.34 % (257433)------------------------------
% 0.22/0.34 % (257433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (257433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (257433)CaDiCaL version: 2.1.3
% 0.22/0.34 % (257433)Termination reason: Instruction limit
% 0.22/0.34 % (257433)Termination phase: Saturation
% 0.22/0.34 % (257433)Time elapsed: 0.004 s
% 0.22/0.34 % (257433)Peak memory usage: 12 MB
% 0.22/0.34 % (257433)Instructions burned: 13 (million)
% 0.22/0.34 % (257429)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2253696076:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.34 % (257432)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3025614891:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.34 % (257429)Instruction limit reached!
% 0.22/0.34 % (257429)------------------------------
% 0.22/0.34 % (257429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (257429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (257429)CaDiCaL version: 2.1.3
% 0.22/0.34 % (257429)Termination reason: Instruction limit
% 0.22/0.34 % (257429)Termination phase: Saturation
% 0.22/0.34 % (257429)Time elapsed: 0.003 s
% 0.22/0.34 % (257429)Peak memory usage: 11 MB
% 0.22/0.34 % (257429)Instructions burned: 5 (million)
% 0.22/0.34 % (257440)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.34 % (257440)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.34 % (257432)Instruction limit reached!
% 0.22/0.34 % (257432)------------------------------
% 0.22/0.34 % (257432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (257432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (257432)CaDiCaL version: 2.1.3
% 0.22/0.34 % (257432)Termination reason: Instruction limit
% 0.22/0.34 % (257432)Termination phase: Saturation
% 0.22/0.34 % (257432)Time elapsed: 0.005 s
% 0.22/0.34 % (257432)Peak memory usage: 12 MB
% 0.22/0.34 % (257432)Instructions burned: 8 (million)
% 0.22/0.34 % (257440)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=545874082:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.34 % (257403) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-257390-257403"...
% 0.22/0.34 % (257447)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=358027283:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.34 % (257403)...printing done.
% 0.22/0.34 % (257400)Instruction limit reached!
% 0.22/0.34 % (257400)------------------------------
% 0.22/0.34 % (257400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (257400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (257400)CaDiCaL version: 2.1.3
% 0.22/0.34 % (257400)Termination reason: Instruction limit
% 0.22/0.34 % (257400)Termination phase: Saturation
% 0.22/0.34 % (257400)Time elapsed: 0.050 s
% 0.22/0.34 % (257400)Peak memory usage: 12 MB
% 0.22/0.34 % (257400)Instructions burned: 87 (million)
% 0.22/0.34 % (257403)Refutation found. Thanks to Tanya!
% 0.22/0.34 % SZS status Theorem for theBenchmark
% 0.22/0.34 % SZS output start Proof for theBenchmark
% 0.22/0.34 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.22/0.34 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.34 thf(type_def_7, type, sK2: $tType).
% 0.22/0.34 thf(type_def_8, type, sK3: $tType).
% 0.22/0.34 thf(func_def_0, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.22/0.34 thf(func_def_1, type, 'const/sets/HAS_SIZE': !>[X0: $tType]:(((X0 > $o) > 'type/nums/num' > $o))).
% 0.22/0.34 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.34 thf(func_def_3, type, 'const/sets/CARD': !>[X0: $tType]:(((X0 > $o) > 'type/nums/num'))).
% 0.22/0.34 thf(func_def_7, type, sK0: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > $o) > (X1 > X0) > (X0 > X1) > X1))).
% 0.22/0.34 thf(func_def_8, type, sK1: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > $o) > (X1 > X0) > (X0 > X1) > X0))).
% 0.22/0.34 thf(func_def_9, type, sK4: (sK2 > $o)).
% 0.22/0.34 thf(func_def_10, type, sK5: (sK2 > sK3)).
% 0.22/0.34 thf(func_def_11, type, sK6: (sK3 > $o)).
% 0.22/0.34 thf(func_def_12, type, sK7: (sK3 > sK2)).
% 0.22/0.34 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.34 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.34 thf(f1,axiom,(
% 0.22/0.34 ! [X0 : $tType,X2 : 'type/nums/num',X1 : (X0 > $o)] : (((('const/sets/CARD' @ X0 @ X1)) = X2) & ('const/sets/FINITE' @ X0 @ X1) = (('const/sets/HAS_SIZE' @ X0 @ X1 @ X2)))),
% 0.22/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_')).
% 0.22/0.34 thf(f2,axiom,(
% 0.22/0.34 ! [X0 : $tType,X1 : $tType,X4 : (X0 > X1),X3 : (X1 > $o),X5 : (X1 > X0),X2 : (X0 > $o)] : ((! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X3) => (('const/sets/IN' @ X0 @ (X5 @ X6) @ X2) & (((X4 @ (X5 @ X6))) = X6))) & ! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X2) => ((((X5 @ (X4 @ X6))) = X6) & ('const/sets/IN' @ X1 @ (X4 @ X6) @ X3)))) => ! [X6 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ X0 @ X2 @ X6)) = (('const/sets/HAS_SIZE' @ X1 @ X3 @ X6))))),
% 0.22/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/BIJECTIONS_HAS_SIZE_EQ_')).
% 0.22/0.34 thf(f3,conjecture,(
% 0.22/0.34 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X5 : (X1 > X0),X3 : (X1 > $o),X4 : (X0 > X1)] : (((('const/sets/FINITE' @ X1 @ X3) | ('const/sets/FINITE' @ X0 @ X2)) & ! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X3) => ((((X4 @ (X5 @ X6))) = X6) & ('const/sets/IN' @ X0 @ (X5 @ X6) @ X2))) & ! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X2) => (('const/sets/IN' @ X1 @ (X4 @ X6) @ X3) & (((X5 @ (X4 @ X6))) = X6)))) => ((('const/sets/CARD' @ X0 @ X2)) = (('const/sets/CARD' @ X1 @ X3))))),
% 0.22/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/BIJECTIONS_CARD_EQ_')).
% 0.22/0.34 thf(f4,negated_conjecture,(
% 0.22/0.34 ~ ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X5 : (X1 > X0),X3 : (X1 > $o),X4 : (X0 > X1)] : (((('const/sets/FINITE' @ X1 @ X3) | ('const/sets/FINITE' @ X0 @ X2)) & ! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X3) => ((((X4 @ (X5 @ X6))) = X6) & ('const/sets/IN' @ X0 @ (X5 @ X6) @ X2))) & ! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X2) => (('const/sets/IN' @ X1 @ (X4 @ X6) @ X3) & (((X5 @ (X4 @ X6))) = X6)))) => ((('const/sets/CARD' @ X0 @ X2)) = (('const/sets/CARD' @ X1 @ X3))))),
% 0.22/0.34 inference(negated_conjecture,[status(cth)],[f3])).
% 0.22/0.34 thf(f5,plain,(
% 0.22/0.34 ! [X0 : $tType,X1 : 'type/nums/num',X2 : (X0 > $o)] : (((('const/sets/CARD' @ X0 @ X2)) = X1) & ('const/sets/FINITE' @ X0 @ X2) = (('const/sets/HAS_SIZE' @ X0 @ X2 @ X1)))),
% 0.22/0.34 inference(rectify,[],[f1])).
% 0.22/0.34 thf(f6,plain,(
% 0.22/0.34 ! [X0 : $tType,X2 : (X0 > $o),X1 : 'type/nums/num'] : ((((('const/sets/CARD' @ X0 @ X2)) = X1) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)) <=> ((('const/sets/HAS_SIZE' @ X0 @ X2 @ X1)) = $true))),
% 0.22/0.34 inference(fool_elimination,[],[f5])).
% 0.22/0.34 thf(f7,plain,(
% 0.22/0.34 ~ ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X4 : (X1 > $o),X5 : (X0 > X1)] : (((('const/sets/FINITE' @ X1 @ X4) | ('const/sets/FINITE' @ X0 @ X2)) & ! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X4) => ((((X5 @ (X3 @ X6))) = X6) & ('const/sets/IN' @ X0 @ (X3 @ X6) @ X2))) & ! [X7 : X0] : (('const/sets/IN' @ X0 @ X7 @ X2) => (('const/sets/IN' @ X1 @ (X5 @ X7) @ X4) & (((X3 @ (X5 @ X7))) = X7)))) => ((('const/sets/CARD' @ X0 @ X2)) = (('const/sets/CARD' @ X1 @ X4))))),
% 0.22/0.34 inference(rectify,[],[f4])).
% 0.22/0.34 thf(f8,plain,(
% 0.22/0.34 ~ ! [X1 : $tType,X0 : $tType,X4 : (X1 > $o),X2 : (X0 > $o),X3 : (X1 > X0),X5 : (X0 > X1)] : ((! [X7 : X0] : (((('const/sets/IN' @ X0 @ X7 @ X2)) = $true) => (((('const/sets/IN' @ X1 @ (X5 @ X7) @ X4)) = $true) & (((X3 @ (X5 @ X7))) = X7))) & ! [X6 : X1] : (((('const/sets/IN' @ X1 @ X6 @ X4)) = $true) => ((((X5 @ (X3 @ X6))) = X6) & ($true = (('const/sets/IN' @ X0 @ (X3 @ X6) @ X2))))) & (((('const/sets/FINITE' @ X1 @ X4)) = $true) | ((('const/sets/FINITE' @ X0 @ X2)) = $true))) => ((('const/sets/CARD' @ X0 @ X2)) = (('const/sets/CARD' @ X1 @ X4))))),
% 0.22/0.34 inference(fool_elimination,[],[f7])).
% 0.22/0.34 thf(f9,plain,(
% 0.22/0.34 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > $o),X4 : (X1 > X0),X5 : (X0 > $o)] : ((! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X3) => (('const/sets/IN' @ X0 @ (X4 @ X6) @ X5) & (((X2 @ (X4 @ X6))) = X6))) & ! [X7 : X0] : (('const/sets/IN' @ X0 @ X7 @ X5) => ((((X4 @ (X2 @ X7))) = X7) & ('const/sets/IN' @ X1 @ (X2 @ X7) @ X3)))) => ! [X8 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ X0 @ X5 @ X8)) = (('const/sets/HAS_SIZE' @ X1 @ X3 @ X8))))),
% 0.22/0.34 inference(rectify,[],[f2])).
% 0.22/0.34 thf(f10,plain,(
% 0.22/0.34 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X4 : (X1 > X0),X5 : (X0 > $o),X3 : (X1 > $o)] : ((! [X7 : X0] : (($true = (('const/sets/IN' @ X0 @ X7 @ X5))) => (((('const/sets/IN' @ X1 @ (X2 @ X7) @ X3)) = $true) & (((X4 @ (X2 @ X7))) = X7))) & ! [X6 : X1] : (((('const/sets/IN' @ X1 @ X6 @ X3)) = $true) => (((('const/sets/IN' @ X0 @ (X4 @ X6) @ X5)) = $true) & (((X2 @ (X4 @ X6))) = X6)))) => ! [X8 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ X0 @ X5 @ X8)) = (('const/sets/HAS_SIZE' @ X1 @ X3 @ X8))))),
% 0.22/0.34 inference(fool_elimination,[],[f9])).
% 0.22/0.34 thf(f11,plain,(
% 0.22/0.34 ? [X1 : $tType,X0 : $tType,X4 : (X1 > $o),X2 : (X0 > $o),X3 : (X1 > X0),X5 : (X0 > X1)] : (((('const/sets/CARD' @ X0 @ X2)) != (('const/sets/CARD' @ X1 @ X4))) & (! [X7 : X0] : (((('const/sets/IN' @ X0 @ X7 @ X2)) != $true) | (((('const/sets/IN' @ X1 @ (X5 @ X7) @ X4)) = $true) & (((X3 @ (X5 @ X7))) = X7))) & ! [X6 : X1] : (((((X5 @ (X3 @ X6))) = X6) & ($true = (('const/sets/IN' @ X0 @ (X3 @ X6) @ X2)))) | ((('const/sets/IN' @ X1 @ X6 @ X4)) != $true)) & (((('const/sets/FINITE' @ X1 @ X4)) = $true) | ((('const/sets/FINITE' @ X0 @ X2)) = $true))))),
% 0.22/0.34 inference(ennf_transformation,[],[f8])).
% 0.22/0.34 thf(f12,plain,(
% 0.22/0.34 ? [X1 : $tType,X0 : $tType,X4 : (X1 > $o),X3 : (X1 > X0),X2 : (X0 > $o),X5 : (X0 > X1)] : ((((('const/sets/FINITE' @ X1 @ X4)) = $true) | ((('const/sets/FINITE' @ X0 @ X2)) = $true)) & ! [X7 : X0] : (((('const/sets/IN' @ X0 @ X7 @ X2)) != $true) | (((('const/sets/IN' @ X1 @ (X5 @ X7) @ X4)) = $true) & (((X3 @ (X5 @ X7))) = X7))) & ((('const/sets/CARD' @ X0 @ X2)) != (('const/sets/CARD' @ X1 @ X4))) & ! [X6 : X1] : (((((X5 @ (X3 @ X6))) = X6) & ($true = (('const/sets/IN' @ X0 @ (X3 @ X6) @ X2)))) | ((('const/sets/IN' @ X1 @ X6 @ X4)) != $true)))),
% 0.22/0.34 inference(flattening,[],[f11])).
% 0.22/0.34 thf(f13,plain,(
% 0.22/0.34 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X4 : (X1 > X0),X5 : (X0 > $o),X3 : (X1 > $o)] : (! [X8 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ X0 @ X5 @ X8)) = (('const/sets/HAS_SIZE' @ X1 @ X3 @ X8))) | (? [X7 : X0] : (($true = (('const/sets/IN' @ X0 @ X7 @ X5))) & ((((X4 @ (X2 @ X7))) != X7) | ((('const/sets/IN' @ X1 @ (X2 @ X7) @ X3)) != $true))) | ? [X6 : X1] : ((((('const/sets/IN' @ X0 @ (X4 @ X6) @ X5)) != $true) | (((X2 @ (X4 @ X6))) != X6)) & ((('const/sets/IN' @ X1 @ X6 @ X3)) = $true))))),
% 0.22/0.34 inference(ennf_transformation,[],[f10])).
% 0.22/0.34 thf(f14,plain,(
% 0.22/0.34 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X4 : (X1 > X0),X5 : (X0 > $o),X3 : (X1 > $o)] : (! [X8 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ X0 @ X5 @ X8)) = (('const/sets/HAS_SIZE' @ X1 @ X3 @ X8))) | ? [X6 : X1] : ((((('const/sets/IN' @ X0 @ (X4 @ X6) @ X5)) != $true) | (((X2 @ (X4 @ X6))) != X6)) & ((('const/sets/IN' @ X1 @ X6 @ X3)) = $true)) | ? [X7 : X0] : (($true = (('const/sets/IN' @ X0 @ X7 @ X5))) & ((((X4 @ (X2 @ X7))) != X7) | ((('const/sets/IN' @ X1 @ (X2 @ X7) @ X3)) != $true))))),
% 0.22/0.34 inference(flattening,[],[f13])).
% 0.22/0.34 thf(f15,plain,(
% 0.22/0.34 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X4 : (X0 > $o),X5 : (X1 > $o)] : (! [X6 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6))) | ? [X7 : X1] : ((((('const/sets/IN' @ X0 @ (X3 @ X7) @ X4)) != $true) | (((X2 @ (X3 @ X7))) != X7)) & ($true = (('const/sets/IN' @ X1 @ X7 @ X5)))) | ? [X8 : X0] : (((('const/sets/IN' @ X0 @ X8 @ X4)) = $true) & ((((X3 @ (X2 @ X8))) != X8) | ($true != (('const/sets/IN' @ X1 @ (X2 @ X8) @ X5))))))),
% 0.22/0.34 inference(rectify,[],[f14])).
% 0.22/0.34 thf(f16,plain,(
% 0.22/0.34 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X4 : (X0 > $o),X5 : (X1 > $o)] : (! [X6 : 'type/nums/num'] : ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6))) | ((((('const/sets/IN' @ X0 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X4)) != $true) | (((X2 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) != ((sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) & ($true = (('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X5)))) | (($true = (('const/sets/IN' @ X0 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X4))) & ((((sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) != ((X3 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))))) | ($true != (('const/sets/IN' @ X1 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X5))))))),
% 0.22/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X8,sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2),skolemize(X8,sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)],[f15])).
% 0.22/0.34 thf(f17,plain,(
% 0.22/0.34 ! [X0 : $tType,X2 : (X0 > $o),X1 : 'type/nums/num'] : (((((('const/sets/CARD' @ X0 @ X2)) = X1) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)) | ((('const/sets/HAS_SIZE' @ X0 @ X2 @ X1)) != $true)) & (((('const/sets/HAS_SIZE' @ X0 @ X2 @ X1)) = $true) | (((('const/sets/CARD' @ X0 @ X2)) != X1) | ((('const/sets/FINITE' @ X0 @ X2)) != $true))))),
% 0.22/0.34 inference(nnf_transformation,[],[f6])).
% 0.22/0.34 thf(f18,plain,(
% 0.22/0.34 ! [X0 : $tType,X2 : (X0 > $o),X1 : 'type/nums/num'] : (((((('const/sets/CARD' @ X0 @ X2)) = X1) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)) | ((('const/sets/HAS_SIZE' @ X0 @ X2 @ X1)) != $true)) & (((('const/sets/HAS_SIZE' @ X0 @ X2 @ X1)) = $true) | ((('const/sets/CARD' @ X0 @ X2)) != X1) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)))),
% 0.22/0.34 inference(flattening,[],[f17])).
% 0.22/0.34 thf(f19,plain,(
% 0.22/0.34 ! [X0 : $tType,X1 : (X0 > $o),X2 : 'type/nums/num'] : (((((('const/sets/CARD' @ X0 @ X1)) = X2) & ((('const/sets/FINITE' @ X0 @ X1)) = $true)) | ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2)) != $true)) & (((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2)) = $true) | ((('const/sets/CARD' @ X0 @ X1)) != X2) | ((('const/sets/FINITE' @ X0 @ X1)) != $true)))),
% 0.22/0.34 inference(rectify,[],[f18])).
% 0.22/0.34 thf(f20,plain,(
% 0.22/0.34 ? [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X0 > X1),X4 : (X1 > $o),X5 : (X1 > X0)] : ((((('const/sets/FINITE' @ X0 @ X2)) = $true) | ((('const/sets/FINITE' @ X1 @ X4)) = $true)) & ! [X6 : X1] : (((('const/sets/IN' @ X1 @ X6 @ X4)) != $true) | (((('const/sets/IN' @ X0 @ (X5 @ X6) @ X2)) = $true) & (((X3 @ (X5 @ X6))) = X6))) & ((('const/sets/CARD' @ X0 @ X2)) != (('const/sets/CARD' @ X1 @ X4))) & ! [X7 : X0] : (((((X5 @ (X3 @ X7))) = X7) & ((('const/sets/IN' @ X1 @ (X3 @ X7) @ X4)) = $true)) | ((('const/sets/IN' @ X0 @ X7 @ X2)) != $true)))),
% 0.22/0.34 inference(rectify,[],[f12])).
% 0.22/0.34 thf(f21,plain,(
% 0.22/0.34 (((('const/sets/FINITE' @ sK2 @ sK4)) = $true) | ((('const/sets/FINITE' @ sK3 @ sK6)) = $true)) & ! [X6 : sK3] : (($true != (('const/sets/IN' @ sK3 @ X6 @ sK6))) | (($true = (('const/sets/IN' @ sK2 @ (sK7 @ X6) @ sK4))) & (((sK5 @ (sK7 @ X6))) = X6))) & ((('const/sets/CARD' @ sK3 @ sK6)) != (('const/sets/CARD' @ sK2 @ sK4))) & ! [X7 : sK2] : (((((sK7 @ (sK5 @ X7))) = X7) & ((('const/sets/IN' @ sK3 @ (sK5 @ X7) @ sK6)) = $true)) | ((('const/sets/IN' @ sK2 @ X7 @ sK4)) != $true))),
% 0.22/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5),skolemize(X4,sK6),skolemize(X5,sK7)],[f20])).
% 0.22/0.34 thf(f22,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : ((((sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) != ((X3 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))))) | ($true != (('const/sets/IN' @ X1 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X5))) | ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6))) | ($true = (('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X5)))) )),
% 0.22/0.34 inference(cnf_transformation,[],[f16])).
% 0.22/0.34 thf(f23,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : (($true = (('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X5))) | ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6))) | ($true = (('const/sets/IN' @ X0 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X4)))) )),
% 0.22/0.34 inference(cnf_transformation,[],[f16])).
% 0.22/0.34 thf(f24,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : (((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6))) | (((X2 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) != ((sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))) | (((sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) != ((X3 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))))) | ($true != (('const/sets/IN' @ X1 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X5))) | ((('const/sets/IN' @ X0 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X4)) != $true)) )),
% 0.22/0.34 inference(cnf_transformation,[],[f16])).
% 0.22/0.34 thf(f25,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X4))) | (((X2 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) != ((sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))) | ((('const/sets/IN' @ X0 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X4)) != $true) | ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6)))) )),
% 0.22/0.34 inference(cnf_transformation,[],[f16])).
% 0.22/0.34 thf(f26,plain,(
% 0.22/0.34 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : (X0 > $o)] : (((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2)) = $true) | ((('const/sets/CARD' @ X0 @ X1)) != X2) | ((('const/sets/FINITE' @ X0 @ X1)) != $true)) )),
% 0.22/0.34 inference(cnf_transformation,[],[f19])).
% 0.22/0.34 thf(f28,plain,(
% 0.22/0.34 ( ! [X0 : $tType,X2 : 'type/nums/num',X1 : (X0 > $o)] : (((('const/sets/HAS_SIZE' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/CARD' @ X0 @ X1)) = X2)) )),
% 0.22/0.34 inference(cnf_transformation,[],[f19])).
% 0.22/0.34 thf(f29,plain,(
% 0.22/0.34 ( ! [X7 : sK2] : (((('const/sets/IN' @ sK3 @ (sK5 @ X7) @ sK6)) = $true) | ((('const/sets/IN' @ sK2 @ X7 @ sK4)) != $true)) )),
% 0.22/0.34 inference(cnf_transformation,[],[f21])).
% 0.22/0.34 thf(f30,plain,(
% 0.22/0.34 ( ! [X7 : sK2] : (((('const/sets/IN' @ sK2 @ X7 @ sK4)) != $true) | (((sK7 @ (sK5 @ X7))) = X7)) )),
% 0.22/0.34 inference(cnf_transformation,[],[f21])).
% 0.22/0.34 thf(f31,plain,(
% 0.22/0.34 ((('const/sets/CARD' @ sK3 @ sK6)) != (('const/sets/CARD' @ sK2 @ sK4)))),
% 0.22/0.34 inference(cnf_transformation,[],[f21])).
% 0.22/0.34 thf(f32,plain,(
% 0.22/0.34 ( ! [X6 : sK3] : (($true != (('const/sets/IN' @ sK3 @ X6 @ sK6))) | (((sK5 @ (sK7 @ X6))) = X6)) )),
% 0.22/0.34 inference(cnf_transformation,[],[f21])).
% 0.22/0.34 thf(f33,plain,(
% 0.22/0.34 ( ! [X6 : sK3] : (($true = (('const/sets/IN' @ sK2 @ (sK7 @ X6) @ sK4))) | ($true != (('const/sets/IN' @ sK3 @ X6 @ sK6)))) )),
% 0.22/0.34 inference(cnf_transformation,[],[f21])).
% 0.22/0.34 thf(f34,plain,(
% 0.22/0.34 ((('const/sets/FINITE' @ sK3 @ sK6)) = $true) | ((('const/sets/FINITE' @ sK2 @ sK4)) = $true)),
% 0.22/0.34 inference(cnf_transformation,[],[f21])).
% 0.22/0.34 thf(f36,plain,(
% 0.22/0.34 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/HAS_SIZE' @ X0 @ X1 @ ('const/sets/CARD' @ X0 @ X1)))) | ((('const/sets/FINITE' @ X0 @ X1)) != $true)) )),
% 0.22/0.34 inference(equality_resolution,[],[f26])).
% 0.22/0.34 thf(f37,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : ((((X2 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) != ((sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))) | ($true = (('const/sets/IN' @ X0 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X4))) | ((('const/sets/IN' @ X0 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X4)) != $true) | ($false = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6))) | ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = $true)) )),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f25])).
% 0.22/0.34 thf(f38,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : ((((X2 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) != ((sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))) | ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = $false) | ((('const/sets/IN' @ X0 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X4)) != $true) | ($true = (('const/sets/IN' @ X0 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X4))) | ($true = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6)))) )),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f25])).
% 0.22/0.34 thf(f39,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : ((((sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) != ((X3 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))))) | ($false = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6))) | ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = $true) | ((('const/sets/IN' @ X0 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X4)) != $true) | ($true != (('const/sets/IN' @ X1 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X5))) | (((X2 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) != ((sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) )),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f24])).
% 0.22/0.34 thf(f40,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : ((((sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) != ((X3 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))))) | (((X2 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)))) != ((sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))) | ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = $false) | ($true != (('const/sets/IN' @ X1 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X5))) | ((('const/sets/IN' @ X0 @ (X3 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X4)) != $true) | ($true = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6)))) )),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f24])).
% 0.22/0.34 thf(f41,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : ((((sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) != ((X3 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))))) | ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = $true) | ($true = (('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X5))) | ($false = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6))) | ($true != (('const/sets/IN' @ X1 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X5)))) )),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f22])).
% 0.22/0.34 thf(f42,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : ((((sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) != ((X3 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))))) | ($true != (('const/sets/IN' @ X1 @ (X2 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)) @ X5))) | ($true = (('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X5))) | ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = $false) | ($true = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6)))) )),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f22])).
% 0.22/0.34 thf(f43,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : (($true = (('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X5))) | ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = $true) | ($false = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6))) | ($true = (('const/sets/IN' @ X0 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X4)))) )),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f23])).
% 0.22/0.34 thf(f44,plain,(
% 0.22/0.34 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1),X3 : (X1 > X0),X6 : 'type/nums/num',X4 : (X0 > $o),X5 : (X1 > $o)] : (($true = (('const/sets/IN' @ X1 @ (sK0 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X5))) | ($true = (('const/sets/HAS_SIZE' @ X0 @ X4 @ X6))) | ($true = (('const/sets/IN' @ X0 @ (sK1 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ X4))) | ((('const/sets/HAS_SIZE' @ X1 @ X5 @ X6)) = $false)) )),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f23])).
% 0.22/0.34 thf(f46,definition,(
% 0.22/0.34 spl8_1 <=> ((('const/sets/FINITE' @ sK2 @ sK4)) = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 0.22/0.34 thf(f50,definition,(
% 0.22/0.34 spl8_2 <=> ((('const/sets/FINITE' @ sK3 @ sK6)) = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.22/0.34 thf(f53,plain,(
% 0.22/0.34 spl8_1 | spl8_2),
% 0.22/0.34 inference(avatar_split_clause,[],[f34,f50,f46])).
% 0.22/0.34 thf(f55,definition,(
% 0.22/0.34 spl8_3 <=> ((('const/sets/CARD' @ sK3 @ sK6)) = (('const/sets/CARD' @ sK2 @ sK4)))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
% 0.22/0.34 thf(f57,plain,(
% 0.22/0.34 ((('const/sets/CARD' @ sK3 @ sK6)) != (('const/sets/CARD' @ sK2 @ sK4))) | spl8_3),
% 0.22/0.34 inference(avatar_component_clause,[],[f55])).
% 0.22/0.34 thf(f58,plain,(
% 0.22/0.34 ~spl8_3),
% 0.22/0.34 inference(avatar_split_clause,[],[f31,f55])).
% 0.22/0.34 thf(f69,plain,(
% 0.22/0.34 ( ! [X0 : $tType,X2 : (sK2 > X0),X3 : (X0 > sK2),X1 : (X0 > $o),X4 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X4)) = $true) | ($true != $true) | ((('const/sets/IN' @ X0 @ (sK1 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3) @ X1)) = $true) | ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X4)) = $false) | (((sK0 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3)) = ((sK7 @ (sK5 @ (sK0 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3)))))) )),
% 0.22/0.34 inference(superposition,[],[f30,f43])).
% 0.22/0.34 thf(f70,plain,(
% 0.22/0.34 ( ! [X0 : $tType,X2 : (sK2 > X0),X3 : (X0 > sK2),X1 : (X0 > $o),X4 : 'type/nums/num'] : ((((sK0 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3)) = ((sK7 @ (sK5 @ (sK0 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3))))) | ((('const/sets/IN' @ X0 @ (sK1 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3) @ X1)) = $true) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X4)) = $true) | ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X4)) = $false)) )),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f69])).
% 0.22/0.34 thf(f73,plain,(
% 0.22/0.34 ( ! [X0 : $tType,X2 : (sK2 > X0),X3 : (X0 > sK2),X1 : (X0 > $o),X4 : 'type/nums/num'] : (($true != $true) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X4)) = $false) | ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X4)) = $true) | ((('const/sets/IN' @ X0 @ (sK1 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3) @ X1)) = $true) | (((sK0 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3)) = ((sK7 @ (sK5 @ (sK0 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3)))))) )),
% 0.22/0.34 inference(superposition,[],[f30,f44])).
% 0.22/0.34 thf(f75,plain,(
% 0.22/0.34 ( ! [X0 : $tType,X2 : (sK2 > X0),X3 : (X0 > sK2),X1 : (X0 > $o),X4 : 'type/nums/num'] : ((((sK0 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3)) = ((sK7 @ (sK5 @ (sK0 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3))))) | ((('const/sets/HAS_SIZE' @ X0 @ X1 @ X4)) = $true) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X4)) = $false) | ((('const/sets/IN' @ X0 @ (sK1 @ X0 @ sK2 @ sK4 @ X1 @ X2 @ X3) @ X1)) = $true)) )),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f73])).
% 0.22/0.34 thf(f88,plain,(
% 0.22/0.34 ( ! [X2 : 'type/nums/num',X0 : (sK3 > $o),X1 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X2)) = $false) | ($true != (('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7)) @ X0))) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7) @ X0))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X2)) = $true) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7) @ X0))) | ((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X1)) = $false) | (((sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7)) != ((sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7))) | ($true = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1)))) )),
% 0.22/0.34 inference(superposition,[],[f37,f70])).
% 0.22/0.34 thf(f93,plain,(
% 0.22/0.34 ( ! [X2 : 'type/nums/num',X0 : (sK3 > $o),X1 : 'type/nums/num'] : (($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7) @ X0))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X2)) = $true) | (((sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7)) != ((sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7))) | ($true = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X2)) = $false) | ((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X1)) = $false) | ($true != (('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7)) @ X0)))) )),
% 0.22/0.34 inference(duplicate_literal_removal,[],[f88])).
% 0.22/0.34 thf(f94,plain,(
% 0.22/0.34 ( ! [X2 : 'type/nums/num',X0 : (sK3 > $o),X1 : 'type/nums/num'] : (($true != (('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7)) @ X0))) | ((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X1)) = $false) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X2)) = $true) | ($true = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X2)) = $false) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7) @ X0)))) )),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f93])).
% 0.22/0.34 thf(f102,definition,(
% 0.22/0.34 spl8_4 <=> ! [X1 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X1)) = $true) | ($false = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition])).
% 0.22/0.34 thf(f103,plain,(
% 0.22/0.34 ( ! [X1 : 'type/nums/num'] : (($false = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X1)) = $true)) ) | ~spl8_4),
% 0.22/0.34 inference(avatar_component_clause,[],[f102])).
% 0.22/0.34 thf(f105,definition,(
% 0.22/0.34 spl8_5 <=> ! [X0 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $false))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition])).
% 0.22/0.34 thf(f106,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $false) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $true)) ) | ~spl8_5),
% 0.22/0.34 inference(avatar_component_clause,[],[f105])).
% 0.22/0.34 thf(f115,plain,(
% 0.22/0.34 ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ ('const/sets/CARD' @ sK2 @ sK4))) = $true) | ($true = $false) | ((('const/sets/FINITE' @ sK2 @ sK4)) != $true) | ~spl8_4),
% 0.22/0.34 inference(superposition,[],[f36,f103])).
% 0.22/0.34 thf(f119,plain,(
% 0.22/0.34 ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ ('const/sets/CARD' @ sK2 @ sK4))) = $true) | ((('const/sets/FINITE' @ sK2 @ sK4)) != $true) | ~spl8_4),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f115])).
% 0.22/0.34 thf(f121,definition,(
% 0.22/0.34 spl8_7 <=> ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ ('const/sets/CARD' @ sK2 @ sK4))) = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition])).
% 0.22/0.34 thf(f123,plain,(
% 0.22/0.34 ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ ('const/sets/CARD' @ sK2 @ sK4))) = $true) | ~spl8_7),
% 0.22/0.34 inference(avatar_component_clause,[],[f121])).
% 0.22/0.34 thf(f125,plain,(
% 0.22/0.34 spl8_7 | ~spl8_1 | ~spl8_4),
% 0.22/0.34 inference(avatar_split_clause,[],[f119,f102,f46,f121])).
% 0.22/0.34 thf(f134,plain,(
% 0.22/0.34 ( ! [X2 : 'type/nums/num',X0 : (sK3 > $o),X1 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X1)) = $true) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7) @ X0))) | ($false = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X2)) = $true) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X2)) = $false) | (((sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7)) != ((sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7))) | ($true != (('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7)) @ X0))) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7) @ X0)))) )),
% 0.22/0.34 inference(superposition,[],[f38,f75])).
% 0.22/0.34 thf(f138,plain,(
% 0.22/0.34 ( ! [X2 : 'type/nums/num',X0 : (sK3 > $o),X1 : 'type/nums/num'] : ((((sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7)) != ((sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X2)) = $false) | ($false = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ($true != (('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7)) @ X0))) | ((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X2)) = $true) | ((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X1)) = $true) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7) @ X0)))) )),
% 0.22/0.34 inference(duplicate_literal_removal,[],[f134])).
% 0.22/0.34 thf(f139,plain,(
% 0.22/0.34 ( ! [X2 : 'type/nums/num',X0 : (sK3 > $o),X1 : 'type/nums/num'] : (($true != (('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7)) @ X0))) | ((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X2)) = $true) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X2)) = $false) | ($false = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ X0 @ sK5 @ sK7) @ X0))) | ((('const/sets/HAS_SIZE' @ sK3 @ X0 @ X1)) = $true)) )),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f138])).
% 0.22/0.34 thf(f145,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != $true) | ((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) != $true) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK6))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X1)) = $false) | ($true = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $false)) )),
% 0.22/0.34 inference(superposition,[],[f94,f29])).
% 0.22/0.34 thf(f146,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $true) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK6))) | ($true = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X1)) = $false) | ((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) != $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $false)) )),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f145])).
% 0.22/0.34 thf(f147,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK6))) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X1)) = $false) | ($true = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $false) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $true)) )),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f146,f43])).
% 0.22/0.34 thf(f149,definition,(
% 0.22/0.34 spl8_8 <=> ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK6)))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition])).
% 0.22/0.34 thf(f151,plain,(
% 0.22/0.34 ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK6))) | ~spl8_8),
% 0.22/0.34 inference(avatar_component_clause,[],[f149])).
% 0.22/0.34 thf(f152,plain,(
% 0.22/0.34 spl8_8 | spl8_5 | spl8_5),
% 0.22/0.34 inference(avatar_split_clause,[],[f147,f105,f105,f149])).
% 0.22/0.34 thf(f159,plain,(
% 0.22/0.34 ($true = $false) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ ('const/sets/CARD' @ sK3 @ sK6))) = $true) | ((('const/sets/FINITE' @ sK3 @ sK6)) != $true) | ~spl8_5),
% 0.22/0.34 inference(superposition,[],[f36,f106])).
% 0.22/0.34 thf(f165,plain,(
% 0.22/0.34 ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ ('const/sets/CARD' @ sK3 @ sK6))) = $true) | ((('const/sets/FINITE' @ sK3 @ sK6)) != $true) | ~spl8_5),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f159])).
% 0.22/0.34 thf(f169,definition,(
% 0.22/0.34 spl8_9 <=> ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ ('const/sets/CARD' @ sK3 @ sK6))) = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition])).
% 0.22/0.34 thf(f171,plain,(
% 0.22/0.34 ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ ('const/sets/CARD' @ sK3 @ sK6))) = $true) | ~spl8_9),
% 0.22/0.34 inference(avatar_component_clause,[],[f169])).
% 0.22/0.34 thf(f174,plain,(
% 0.22/0.34 ~spl8_2 | spl8_9 | ~spl8_5),
% 0.22/0.34 inference(avatar_split_clause,[],[f165,f105,f169,f50])).
% 0.22/0.34 thf(f180,plain,(
% 0.22/0.34 ($true != $true) | ((('const/sets/CARD' @ sK3 @ sK6)) = (('const/sets/CARD' @ sK2 @ sK4))) | ~spl8_7),
% 0.22/0.34 inference(superposition,[],[f28,f123])).
% 0.22/0.34 thf(f185,plain,(
% 0.22/0.34 ((('const/sets/CARD' @ sK3 @ sK6)) = (('const/sets/CARD' @ sK2 @ sK4))) | ~spl8_7),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f180])).
% 0.22/0.34 thf(f193,plain,(
% 0.22/0.34 $false | (spl8_3 | ~spl8_7)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f185,f57])).
% 0.22/0.34 thf(f194,plain,(
% 0.22/0.34 spl8_3 | ~spl8_7),
% 0.22/0.34 inference(avatar_contradiction_clause,[],[f193])).
% 0.22/0.34 thf(f198,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != $true) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK6))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $false) | ((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) != $true) | ($false = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X1)) = $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $true)) )),
% 0.22/0.34 inference(superposition,[],[f139,f29])).
% 0.22/0.34 thf(f199,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) != $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $true) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK6))) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X1)) = $true) | ($false = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $false)) )),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f198])).
% 0.22/0.34 thf(f200,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($false = (('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X1))) | ($true = (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK6))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $false) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X1)) = $true)) )),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f199,f44])).
% 0.22/0.34 thf(f201,plain,(
% 0.22/0.34 spl8_4 | spl8_8 | spl8_4),
% 0.22/0.34 inference(avatar_split_clause,[],[f200,f102,f149,f102])).
% 0.22/0.34 thf(f231,plain,(
% 0.22/0.34 (((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) = ((sK5 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ($true != $true) | ~spl8_8),
% 0.22/0.34 inference(superposition,[],[f32,f151])).
% 0.22/0.34 thf(f232,plain,(
% 0.22/0.34 (((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) = ((sK5 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ~spl8_8),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f231])).
% 0.22/0.34 thf(f234,definition,(
% 0.22/0.34 spl8_11 <=> (((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) = ((sK5 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)))))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition])).
% 0.22/0.34 thf(f236,plain,(
% 0.22/0.34 (((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) = ((sK5 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ~spl8_11),
% 0.22/0.34 inference(avatar_component_clause,[],[f234])).
% 0.22/0.34 thf(f237,plain,(
% 0.22/0.34 spl8_11 | ~spl8_8),
% 0.22/0.34 inference(avatar_split_clause,[],[f232,f149,f234])).
% 0.22/0.34 thf(f240,plain,(
% 0.22/0.34 ((('const/sets/CARD' @ sK3 @ sK6)) = (('const/sets/CARD' @ sK2 @ sK4))) | ($true != $true) | ~spl8_9),
% 0.22/0.34 inference(superposition,[],[f28,f171])).
% 0.22/0.34 thf(f245,plain,(
% 0.22/0.34 ((('const/sets/CARD' @ sK3 @ sK6)) = (('const/sets/CARD' @ sK2 @ sK4))) | ~spl8_9),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f240])).
% 0.22/0.34 thf(f253,plain,(
% 0.22/0.34 $false | (spl8_3 | ~spl8_9)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f245,f57])).
% 0.22/0.34 thf(f254,plain,(
% 0.22/0.34 spl8_3 | ~spl8_9),
% 0.22/0.34 inference(avatar_contradiction_clause,[],[f253])).
% 0.22/0.34 thf(f267,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (($true != (('const/sets/IN' @ sK2 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK4))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $true) | ((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) = $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $false) | (((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) != ((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)))) ) | ~spl8_11),
% 0.22/0.34 inference(superposition,[],[f41,f236])).
% 0.22/0.34 thf(f268,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (($true != (('const/sets/IN' @ sK2 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK4))) | ((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) = $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $false) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $true)) ) | ~spl8_11),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f267])).
% 0.22/0.34 thf(f270,definition,(
% 0.22/0.34 spl8_14 <=> ($true = (('const/sets/IN' @ sK2 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK4)))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition])).
% 0.22/0.34 thf(f271,plain,(
% 0.22/0.34 ($true = (('const/sets/IN' @ sK2 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK4))) | ~spl8_14),
% 0.22/0.34 inference(avatar_component_clause,[],[f270])).
% 0.22/0.34 thf(f272,plain,(
% 0.22/0.34 ($true != (('const/sets/IN' @ sK2 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK4))) | spl8_14),
% 0.22/0.34 inference(avatar_component_clause,[],[f270])).
% 0.22/0.34 thf(f274,definition,(
% 0.22/0.34 spl8_15 <=> ((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_15])],[avatar_definition])).
% 0.22/0.34 thf(f276,plain,(
% 0.22/0.34 ((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) = $true) | ~spl8_15),
% 0.22/0.34 inference(avatar_component_clause,[],[f274])).
% 0.22/0.34 thf(f277,plain,(
% 0.22/0.34 ~spl8_14 | spl8_5 | spl8_15 | ~spl8_11),
% 0.22/0.34 inference(avatar_split_clause,[],[f268,f234,f274,f105,f270])).
% 0.22/0.34 thf(f282,plain,(
% 0.22/0.34 ($true != $true) | ($true != (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK6))) | spl8_14),
% 0.22/0.34 inference(superposition,[],[f272,f33])).
% 0.22/0.34 thf(f283,plain,(
% 0.22/0.34 ($true != (('const/sets/IN' @ sK3 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK6))) | spl8_14),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f282])).
% 0.22/0.34 thf(f284,plain,(
% 0.22/0.34 $false | (~spl8_8 | spl8_14)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f283,f151])).
% 0.22/0.34 thf(f285,plain,(
% 0.22/0.34 ~spl8_8 | spl8_14),
% 0.22/0.34 inference(avatar_contradiction_clause,[],[f284])).
% 0.22/0.34 thf(f286,plain,(
% 0.22/0.34 ($true != $true) | (((sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) = ((sK7 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ~spl8_15),
% 0.22/0.34 inference(superposition,[],[f30,f276])).
% 0.22/0.34 thf(f287,plain,(
% 0.22/0.34 (((sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) = ((sK7 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ~spl8_15),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f286])).
% 0.22/0.34 thf(f289,definition,(
% 0.22/0.34 spl8_16 <=> (((sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) = ((sK7 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)))))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_16])],[avatar_definition])).
% 0.22/0.34 thf(f291,plain,(
% 0.22/0.34 (((sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) = ((sK7 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ~spl8_16),
% 0.22/0.34 inference(avatar_component_clause,[],[f289])).
% 0.22/0.34 thf(f292,plain,(
% 0.22/0.34 spl8_16 | ~spl8_15),
% 0.22/0.34 inference(avatar_split_clause,[],[f287,f274,f289])).
% 0.22/0.34 thf(f304,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : ((((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) != ((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))) | ((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) = $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $true) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $false) | ($true != (('const/sets/IN' @ sK2 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK4)))) ) | ~spl8_11),
% 0.22/0.34 inference(superposition,[],[f42,f236])).
% 0.22/0.34 thf(f308,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) = $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $true) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $false) | ($true != (('const/sets/IN' @ sK2 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK4)))) ) | ~spl8_11),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f304])).
% 0.22/0.34 thf(f334,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $true) | ($true != (('const/sets/IN' @ sK2 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK4))) | (((sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) != ((sK7 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ((('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK6)) != $true) | (((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) != ((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $false)) ) | ~spl8_11),
% 0.22/0.34 inference(superposition,[],[f39,f236])).
% 0.22/0.34 thf(f339,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (((('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK6)) != $true) | ($true != (('const/sets/IN' @ sK2 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK4))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $true) | (((sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) != ((sK7 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $false)) ) | ~spl8_11),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f334])).
% 0.22/0.34 thf(f341,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : ((((sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) != ((sK7 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $true) | ((('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK6)) != $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $false)) ) | (~spl8_11 | ~spl8_14)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f339,f271])).
% 0.22/0.34 thf(f342,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $false) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $true) | ((('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK6)) != $true)) ) | (~spl8_11 | ~spl8_14 | ~spl8_16)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f341,f291])).
% 0.22/0.34 thf(f344,definition,(
% 0.22/0.34 spl8_20 <=> ((('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK6)) = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_20])],[avatar_definition])).
% 0.22/0.34 thf(f345,plain,(
% 0.22/0.34 ((('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK6)) = $true) | ~spl8_20),
% 0.22/0.34 inference(avatar_component_clause,[],[f344])).
% 0.22/0.34 thf(f346,plain,(
% 0.22/0.34 ((('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK6)) != $true) | spl8_20),
% 0.22/0.34 inference(avatar_component_clause,[],[f344])).
% 0.22/0.34 thf(f347,plain,(
% 0.22/0.34 ~spl8_20 | spl8_5 | ~spl8_11 | ~spl8_14 | ~spl8_16),
% 0.22/0.34 inference(avatar_split_clause,[],[f342,f289,f270,f234,f105,f344])).
% 0.22/0.34 thf(f355,plain,(
% 0.22/0.34 ((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) != $true) | ($true != $true) | spl8_20),
% 0.22/0.34 inference(superposition,[],[f346,f29])).
% 0.22/0.34 thf(f356,plain,(
% 0.22/0.34 ((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) != $true) | spl8_20),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f355])).
% 0.22/0.34 thf(f357,plain,(
% 0.22/0.34 $false | (~spl8_15 | spl8_20)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f356,f276])).
% 0.22/0.34 thf(f358,plain,(
% 0.22/0.34 ~spl8_15 | spl8_20),
% 0.22/0.34 inference(avatar_contradiction_clause,[],[f357])).
% 0.22/0.34 thf(f398,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $true) | (((sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) != ((sK7 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ((('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK6)) != $true) | ($true != (('const/sets/IN' @ sK2 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK4))) | (((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) != ((sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $false)) ) | ~spl8_11),
% 0.22/0.34 inference(superposition,[],[f40,f236])).
% 0.22/0.34 thf(f401,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (($true != (('const/sets/IN' @ sK2 @ (sK7 @ (sK1 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK4))) | ((('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK6)) != $true) | ((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $true) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $false) | (((sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) != ((sK7 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)))))) ) | ~spl8_11),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f398])).
% 0.22/0.34 thf(f409,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $true) | ((('const/sets/IN' @ sK2 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7) @ sK4)) = $true) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $false)) ) | (~spl8_11 | ~spl8_14)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f308,f271])).
% 0.22/0.34 thf(f410,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $true) | (((sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) != ((sK7 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ((('const/sets/IN' @ sK3 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) @ sK6)) != $true) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $false)) ) | (~spl8_11 | ~spl8_14)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f401,f271])).
% 0.22/0.34 thf(f416,plain,(
% 0.22/0.34 spl8_15 | spl8_4 | ~spl8_11 | ~spl8_14),
% 0.22/0.34 inference(avatar_split_clause,[],[f409,f270,f234,f102,f274])).
% 0.22/0.34 thf(f417,plain,(
% 0.22/0.34 ( ! [X0 : 'type/nums/num'] : (((('const/sets/HAS_SIZE' @ sK3 @ sK6 @ X0)) = $true) | (((sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7)) != ((sK7 @ (sK5 @ (sK0 @ sK3 @ sK2 @ sK4 @ sK6 @ sK5 @ sK7))))) | ((('const/sets/HAS_SIZE' @ sK2 @ sK4 @ X0)) = $false)) ) | (~spl8_11 | ~spl8_14 | ~spl8_20)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f410,f345])).
% 0.22/0.34 thf(f418,plain,(
% 0.22/0.34 spl8_4 | ~spl8_16 | ~spl8_11 | ~spl8_14 | ~spl8_20),
% 0.22/0.34 inference(avatar_split_clause,[],[f417,f344,f270,f234,f289,f102])).
% 0.22/0.34 cnf(s1, plain, spl8_1 | spl8_2, inference(sat_conversion,[],[f53])).
% 0.22/0.34 cnf(s2, plain, ~spl8_3, inference(sat_conversion,[],[f58])).
% 0.22/0.34 cnf(s5, plain, ~spl8_1 | ~spl8_4 | spl8_7, inference(sat_conversion,[],[f125])).
% 0.22/0.34 cnf(s6, plain, spl8_5 | spl8_5 | spl8_8, inference(sat_conversion,[],[f152])).
% 0.22/0.34 cnf(s7, plain, spl8_5 | spl8_8, inference(rat,[],[s6])).
% 0.22/0.34 cnf(s11, plain, ~spl8_2 | ~spl8_5 | spl8_9, inference(sat_conversion,[],[f174])).
% 0.22/0.34 cnf(s15, plain, spl8_3 | ~spl8_7, inference(sat_conversion,[],[f194])).
% 0.22/0.34 cnf(s21, plain, spl8_4 | spl8_4 | spl8_8, inference(sat_conversion,[],[f201])).
% 0.22/0.34 cnf(s22, plain, spl8_4 | spl8_8, inference(rat,[],[s21])).
% 0.22/0.34 cnf(s25, plain, ~spl8_8 | spl8_11, inference(sat_conversion,[],[f237])).
% 0.22/0.34 cnf(s29, plain, spl8_3 | ~spl8_9, inference(sat_conversion,[],[f254])).
% 0.22/0.34 cnf(s32, plain, spl8_5 | ~spl8_11 | ~spl8_14 | spl8_15, inference(sat_conversion,[],[f277])).
% 0.22/0.34 cnf(s33, plain, ~spl8_8 | spl8_14, inference(sat_conversion,[],[f285])).
% 0.22/0.34 cnf(s34, plain, ~spl8_15 | spl8_16, inference(sat_conversion,[],[f292])).
% 0.22/0.34 cnf(s38, plain, spl8_5 | ~spl8_11 | ~spl8_14 | ~spl8_16 | ~spl8_20, inference(sat_conversion,[],[f347])).
% 0.22/0.34 cnf(s39, plain, ~spl8_15 | spl8_20, inference(sat_conversion,[],[f358])).
% 0.22/0.34 cnf(s45, plain, spl8_4 | ~spl8_11 | ~spl8_14 | spl8_15, inference(sat_conversion,[],[f416])).
% 0.22/0.34 cnf(s46, plain, spl8_4 | ~spl8_11 | ~spl8_14 | ~spl8_16 | ~spl8_20, inference(sat_conversion,[],[f418])).
% 0.22/0.34 cnf(s47, plain, ~spl8_9, inference(rat,[],[s29,s2])).
% 0.22/0.34 cnf(s48, plain, ~spl8_7, inference(rat,[],[s15,s2])).
% 0.22/0.34 cnf(s49, plain, ~spl8_11 | spl8_5 | ~spl8_14, inference(rat,[],[s38,s34,s39,s32])).
% 0.22/0.34 cnf(s50, plain, spl8_5, inference(rat,[],[s49,s25,s33,s7])).
% 0.22/0.34 cnf(s51, plain, ~spl8_2, inference(rat,[],[s11,s47,s50])).
% 0.22/0.34 cnf(s52, plain, spl8_1, inference(rat,[],[s1,s51])).
% 0.22/0.34 cnf(s53, plain, ~spl8_4, inference(rat,[],[s5,s48,s52])).
% 0.22/0.34 cnf(s54, plain, spl8_8, inference(rat,[],[s22,s53])).
% 0.22/0.34 cnf(s56, plain, spl8_14, inference(rat,[],[s33,s54])).
% 0.22/0.34 cnf(s57, plain, spl8_11, inference(rat,[],[s25,s54])).
% 0.22/0.34 cnf(s60, plain, spl8_15, inference(rat,[],[s45,s56,s53,s57])).
% 0.22/0.34 cnf(s61, plain, spl8_20, inference(rat,[],[s39,s60])).
% 0.22/0.34 cnf(s62, plain, spl8_16, inference(rat,[],[s34,s60])).
% 0.22/0.34 cnf(s64, plain, $false, inference(rat,[],[s46,s56,s57,s53,s62,s61])).
% 0.22/0.34 thf(f419,plain,(
% 0.22/0.34 $false),
% 0.22/0.34 inference(avatar_sat_refutation,[],[s64])).
% 0.22/0.34 % SZS output end Proof for theBenchmark
% 0.22/0.34 % (257403)------------------------------
% 0.22/0.34 % (257403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (257403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (257403)CaDiCaL version: 2.1.3
% 0.22/0.34 % (257403)Termination reason: Refutation
% 0.22/0.34 % (257403)Time elapsed: 0.048 s
% 0.22/0.34 % (257403)Peak memory usage: 13 MB
% 0.22/0.34 % (257403)Instructions burned: 84 (million)
% 0.22/0.34 % (257390)Success in time 0.083 s
% 0.22/0.34 % Vampire exiting
%------------------------------------------------------------------------------